Convergence of an Unfeasible Primal-Dual Interior-Point Method for ConvexProgramming

摘要

The unfeasible primal dual algorithm for smooth convex programming recentlyintroduced by Vial is considered. It is shown under mild assumptions, that a SUMT (Sequential Unconstrained Minimization Technique) or 'long step path following' version of the algorithm is globally convergent. The steplength on each iteration is based on a merit function which is a modification of the potential function proposed by Vial.